The Purpose and the Structure

Back propagation (BP) network is the most widely used supervised learning network composed of 3 (or more) layers: the input, hidden and output layers containing $n$, $l$ and $m$ nodes, respectively.

Each node is fully connected to all nodes in the previous layer. The weights between the input and hidden layers and the hidden and output layers are obtained through a training process using training data

$$\{ (X_p, Y_p),\;\;p=1,\cdots,N \}$$

where $X=[x_i,\cdots,x_n]^T$ and $X=[y_i,\cdots,y_m]^T$ are n-D and m-D vectors which form a pattern pair representing an input pattern and the desired output corresponding to the input.

The purpose is to train the network so that it will always output a pattern $Y_k$ when the current input $X$ is most similar to $X_k$. So it can be used as a pattern associator or a pattern classifier.